# Sketching regions in the complex plane

• November 20th 2011, 06:17 PM
andrew2322
Sketching regions in the complex plane
Hi all I have the following problem:

Sketch the following region in the complex plane:

|z+1+i| greater than or equal to 1

i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?
• November 20th 2011, 06:32 PM
TKHunny
Re: Sketching regions in the complex plane
|z+1+i| >= 1

|z-(-1-i)| >= 1

The distance from -1-i is greater than or equal to 1. This is not a circle. It is an entire plane with an open circle removed.

You are close. Your circle is the edge of the solution region. Excepting the switch to cartesian coordinates, your work seems reasonable.
• November 20th 2011, 06:33 PM
Prove It
Re: Sketching regions in the complex plane
Quote:

Originally Posted by andrew2322
Hi all I have the following problem:

Sketch the following region in the complex plane:

|z+1+i| greater than or equal to 1

i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?

The solution is the circle $\displaystyle (x + 1)^2 + (y + 1)^2 = 1$ and all points outside the circle as well.